Question 1192717
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Drawing:
<img src = "https://i.imgur.com/wVwdBpP.png">
a = x = horizontal leg
b = 8 = vertical leg
c = 2x-2 = hypotenuse 


Apply the Pythagorean Theorem
{{{a^2 + b^2 = c^2}}}


{{{x^2 + 8^2 = (2x-2)^2}}}


{{{x^2+64 = 4x^2-8x+4}}}


{{{0 = 4x^2-8x+4-64 - x^2}}}


{{{0 = 3x^2-8x-60}}}


{{{3x^2-8x-60 = 0}}}


The last equation is in the form {{{ax^2+bx+c = 0}}} with
a = 3
b = -8
c = -60


Use the quadratic formula
{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(-8)+-sqrt((-8)^2-4(3)(-60)))/(2(3))}}}


{{{x = (8+-sqrt(784))/(6)}}}


{{{x = (8+-    28)/(6)}}}


{{{x = (8+28)/(6)}}} or {{{x = (8-28)/(6)}}}


{{{x = (36)/(6)}}} or  {{{x = (-20)/(6)}}}


{{{x = 6}}} or  {{{x = -10/3 = -3.33}}} approximately
Ignore the negative result because negative side lengths aren't possible.


This x value then leads to
ladder length = 2x-2 = 2(6)-2 = 12-2 = 10


We have a 6-8-10 right triangle.


Answer: 
<font color=red>The ladder is 10 feet long</font>
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